$**$ONLY $9$ and $11$ PLEASE$**$

$9$ Consider a four$-$step serial process with the number of workers at each step and processing times given in the following table.

$\backslash$table$[[$Process Step,Number of Workers,Time per Customer $($in Minutes$)],[1,1,5],[2,5,15],[4,3,10]]$

Assuming that the process starts out empty and is worker$-$paced, how long will it take $($in minutes$)$ to serve $20$ customers?

LO$3-410.$ An automated car wash serves customers with the following serial process: pre$-$treat, wash, rinse, wax, hand dry. Each of these steps is performed by a dedicated machine except for the hand$-$dry step, which is performed manually on each car by one of three workers. The steps of the process have the following processing times:

a$.$ Pre$-$treat: $1$ minute per car

b$.$ Wash: $5$ minutes per car

c$.$ Rinse: $2$ minutes per car

d$.$ Wax: $3$ minutes per car

e$.$ Hand dry: $8$ minutes per car

a$.$ If the car wash has a demand of $15$ cars per hour, what is the flow rate of the process?

b$.$ If the car wash has a demand of $1$

$11.$ The local driver's license center processes applications for driver's license renewals through the following three steps. First, the customer registers with the receptionist, who updates the customer's information in the database. This first step takes $2$ minutes per customer. Then, the customer visits one of two cashiers to pay the associated fees for the license renewal. This takes $8$ minutes per customer because several forms must be printed from the computer and signed by the customer. Finally, the customer visits one of three license processing stations where the customer's picture is taken and the license is printed. This final step takes $15$ minutes per customer.

a$.$ Assuming unlimited demand, what is the flow rate of the process in customers per hour?

b$.$ Assuming unlimited demand, what would the new flow rate be if the center added one server to the bottleneck resource?